The aim of this paper is to find an efficient strategy to provide local services for wind energy systems (i.e., regulate DC line voltage, active power, reactive power), frequency stability and support in both frequency deviation (using droop control) and rate of change of frequency (RoCoF) from generating units when it is used in an interconnected power as well as isolated ones. In order to achieve the research objectives, different strategies were studied. It's about the modeling of Permanent Magnet Synchronous Generator (PMSG) based on variable speed wind system connected grid using back to back converters and systems control. The aim of the present paper is that of analysing the possible contribution of variable speed wind generating units in frequency support, by means of the definition of dedicated control strategies to be implemented at power electronic level. Then, the paper also proposes the integration of inertial and droop frequency controller in order to define a control strategy capable of emulating the frequency response behaviour of a traditional generating unit. Sufficient conditions are derived for robust stabilization in the sense of Lyapunov stability and are formulated in Linear Matrix Inequalities (LMIs). The performances and limits of the proposed controller are evaluated by means of dedicated simulations.